Holographic QFTs on S2×S2, spontaneous symmetry breaking and Efimov saddle points

Abstract

Holographic CFTs and holographic RG flows on space-time manifolds which are d-dimensional products of spheres are investigated. On the gravity side, this corresponds to Einstein-dilaton gravity on an asymptotically AdSd+1 geometry, foliated by a product of spheres. We focus on holographic theories on S2× S2, we show that the only regular five-dimensional bulk geometries have an IR endpoint where one of the sphere shrinks to zero size, while the other remains finite. In the Z2-symmetric limit, where the two spheres have the same UV radii, we show the existence of a infinite discrete set of regular solutions, satisfying an Efimov-like discrete scaling. The Z2-symmetric solution in which both spheres shrink to zero at the endpoint is singular, whereas the solution with lowest free energy is regular and breaks Z2 symmetry spontaneously. We explain this phenomenon analytically by identifying an unstable mode in the bulk around the would-be Z2-symmetric solution. The space of theories have two branches that are connected by a conifold transition in the bulk, which is regular and correspond to a quantum first order transition. Our results also imply that AdS5 does not admit a regular slicing by S2× S2.

Revisiting Coleman-de Luccia transitions in the AdS regime using holography

“…There may be a distributional limit for the source term which exactly matches the behavior of the CdL solution as Λ → ∞, but this is not evident 53. Similar solutions where discussed for general S d 1 × S d 2 foliations in pure gravity[51], and recently for S 2 × S 2 foliations in Einstein-dilaton theory[52].…”

Holographic CFTs on AdSd × Sn and conformal defects

“…Efimov resonances were also found that were explored in [35] to generate a class of associated black hole solutions. The general case of QFTs on S 2 × S 2 was addressed in [17].…”

Revisiting Coleman-de Luccia transitions in the AdS regime using holography

“…We can instead define the boundary conditions on the gravity side in order to accommodate the CdL geometry as an allowed solution. Provided one can do this consistently, 52 this defines a different field theory on the cylinder, which does not admit the global AdS solution as one its states. This theory can only be extended up to a finite global time, at which point the time-evolution reaches a singularity as a consequence of an infinite instantaneous "kick" at ψ = π/2.…”

“…The relevant expansions are given in [13,16] and we refer the reader to these works for details. Without loss of generality we consider a UV fixed point at an extremum of V at ϕ = 0 with the potential in the vicinity 53 Similar solutions where discussed for general S d 1 × S d 2 foliations in pure gravity [51], and recently for S 2 × S 2 foliations in Einstein-dilaton theory [52].…”